Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus

[@mustafizurrahman5699]

Sir I had studied this topic in 1998 or 1999 but couldn't fathom anything. After 25 years, when I am 47 years old, I have been able to understand the intuition. Thank you awfully for enthralling explanation

[@abnereliberganzahernandez6337]

that is very sad man

[@MahmudulhasanMunna-e2l]

what are you doing now sir. seems like ur bangladeshi thats why im asking . where did you studied from . im curently a fresher

[@kieranvelasquez5670]

This is how every math lecture should be: 1.what this looks like/does 2.how to solve/do the problem 3.what this applies to Awesome video made this theorem tie together everything from multi variable calculus so well!

[@bensonjordan103]

Sorry to be off topic but does anybody know of a way to log back into an instagram account..? I was stupid lost my password. I would love any assistance you can give me

[@deanxavier9552]

@Benson Jordan Instablaster ;)

[@bensonjordan103]

@Dean Xavier i really appreciate your reply. I got to the site on google and im trying it out atm. Takes quite some time so I will reply here later with my results.

[@nitinreganti8033]

@@bensonjordan103 did it work!

[@agrajyadav2951]

Nah i think that a lecture that introduces an idea should start with a question, and build up to the theorem without exposing it first hand. That makes it much more interactive and helps us appreciate the beauty of the idea

[@pankajjkumar369]

Your geometric presentation is mind blowing.

[@naman4067]

You can plot this on maple calculator too

[@bzboii]

I've been stoked for this

[@DrTrefor]

oh u:D

[@agrajyadav2951]

Heck yeah lol

[@ahmeds5181]

This channel deserves a million subscriberd!! Highly underrated channel..

[@keyamoni1602]

Whenever i'm having problem with understanding vector calculus or others complicated maths i come here and my doubt gets cleared. This channel is like a lighthouse. Whenever i lose my way it helps me.

[@tasninnewaz6790]

Geometric Intuition gives me geometric feeling. Thank you Trefor!

[@NumbToons]

3:20 Words of wisdom. 'Tendency to curl withiiiiin the surface' HOOOLY MOTHER OF ACCURATE DESCRIPTION.

[@abstractnonsense3253]

You are well on your way to having the overall best set of video lectures on KZbin about the core of university mathematics. Discrete Mathematics, Linear Algebra, Calculus 1, and Calculus 2 are done. Calculus 3 is almost done. All there is left is Complex Analysis, Differential Equations, and Probability & Statistics. Really great work! Impressive to anyone who knows how challenging it is to teach mathematics!

[@DrTrefor]

Thank you! That....uh....is the plan:D Next up is differential equations:)

[@krupt5995]

@@DrTrefor You are awesome dude. And what amazes me is how you can keep a happy, energetic and passionate smile the whole time you are talking. Amazing teaching skills

[@kozukioden2406]

Forget about the maths, you need to teach me how to grow a beard like this

[@Dr.MuhammadZubair-p6z]

Dear Dr. mostly I am watching your lectures, in each lecture I realize that your geometrical representation of the problem is mind blowing and amazing.

[@manojsahoo8303]

Have no words to praise u sir

[@chaithrapai4266]

Lots of love and respect from India.....♥️♥️♥️♥️

[@Chomusuke71]

So lucky to get this in my first year itself...beautiful playlist sir!!

[@DrTrefor]

Thank you so much

[@layd_bak]

Amazing video Trevor! I'm blown away by your conscientious explanations!

[@judepazier4491]

I have begun watching your videos and this all is beginning to make so much sense! Vector calculus can get really abstract/difficult to picture but you made it clear and precise. Thank you for sharing!

[@AnkurSingh-cv1ls]

that's what i was looking for......perfect explanation and all these theorems amazed me......beautiful

[@DrTrefor]

Isn’t it so pretty?

[@AnkurSingh-cv1ls]

@@DrTrefor it is and so does your explanation......really loved it!!

[@spiderkent]

I never really understand the idea behind the theory until I watch this video. Thank you very much.

[@jacobstarr9010]

Hey man I’ve commented here before but just wanted to let me know you helped me ace my Calc 3 final and get a 99% overall in the class. Thank you for your work.

[@DrTrefor]

Amazing, congrats!!

[@transcendingvictor]

Amazing and enlightening video, it is like if the strange relations the Stoke's and Green's theorems describe now made sense. Thank you very much!!

[@sambuddharanjankhanra376]

I chose ur video over kan academy's video keep up the good work

[@dodo-js5gw]

Thanks a lot ! It is much more intuitive now ! Hello from France :D

[@user-wu8yq1rb9t]

I just watched and enjoyed! And for me, when I'm Watching your videos, it's just look like I'm watching "Big Bang theory" or "Friends" series. Thank you so much 💓

[@timeless_tales2000]

I think I finally found the channel I need to visualize my maths imagination.

[@briandwi2504]

Fantastic. Such a great play list. I have learned so much!

[@sergiolucas38]

Amazing video as always, finally i got to these advanced concepts, so crucial to understand field fenomena in physics, thanks :)

[@jacobstarr9010]

After nearly a semester of Calc 3 I’ve found that Stokes theorem is basically the final boss of Calc 3

[@shubhamg23]

Brilliant!! The beauty with which you connected the two thrms...🔥🔥🔥🔥🔥

[@DrTrefor]

Isn’t it cool!?

[@shubhamg23]

@@DrTrefor Certainly!!..The Instructor As Well👍🤩

[@sureshpatel-sg2xw]

@@DrTrefor its cool and fun too

[@raghuramabl6729]

Thanks a lot, you cleared my confusion regarding what exactly is going on when we apply curl on each point of the surface once again thank you 🙌👌🙏

[@Chomusuke71]

This is pure gold!!

[@DrTrefor]

Thank you so much!

[@akuo0708]

this is insanely good

[@tendi.rutsate]

Love the way you explain. Thank you!

[@DrTrefor]

You are so welcome!

[@sumitkumarsahoo7601]

AWESOME, great explanation, doing a great job

[@qamarmoavia4031]

Thank U so much Dr . Keep going ........

[@woodychelton5590]

really like the visualization, great stuff

[@el_andrius]

Thanks for such rich experience!

[@Kottam_Yallawa]

Fluid kinematics is all about vector calculus and now i learnt both 🙂

[@eslamelsofany2470]

thank you for these amazing videos

[@DrTrefor]

You’re most welcome!!

[@mmariokart231]

Ah! Thank you so much! That really helps tie it together

[@Aaron-lp3zt]

Stokes' theorem is lowkey 🔥

[@DrTrefor]

It really is:D

[@Aaron-lp3zt]

@@DrTrefor He really did my boi Green dirty with that generalization tho

[@geoffreyfaust3443]

Another great video, Dr. B! FYI, we non-Canadians are jarred more by your pronunciation of "corollaries" than of "zed". Cheers! G :

[@RUDRARAKESHKUMARGOHIL]

if not understood or a absence of feeling is lacking at some point you may surely watch niltime animation of stokes theorem it will surely fill the loop hole....by the way a great explanation thankyou guruji...

[@richarichi]

at 4:30, can someone please explain what is the k component of the curl? I saw the previous video but still don't understand about that part.

[@abbasibrahim9435]

Although, its a bit late. The surface in 4:30 is dxdy. And the normal vector along the surface is k component

[@Dr.MuhammadZubair-p6z]

Dear Dr. can you tell me the code how to plot the vector field of 2D or 3D vector in GeoGebra App

[@jlpsinde]

Love from Portugal! Realy top

[@vibudha_keshava]

I'm currently doing my PhD and deal with Stokes' theorem a lot. Particularly using partial integration and product rule on Stokes' theorem to regularize certain singular integrals in Boundary Element Method. Would love for some discussion and exchanges with you :)

[@football4d149]

So nice of you amazing video amazing feeling

[@DrTrefor]

Thank you so much!

[@brendan12882]

3:56 clounter what now? :O

[@miguelaphan58]

You SEE there are profesors..and Masters ..Bazzet for instance..is a master..a Big one

[@majidalishabbeer]

Truly immaculate!

[@djredrover]

Hi Dr. Bazett, do you have any plans on doing any videos on linear algebra, specially state space modelling of rockets dynamics and transition between different coordinates and quaternions? I would absolutely LOVE your take on these topics. Thanks again for you wonderful channel.

[@DrTrefor]

I do have a linear algebra playlist, but probably not something as specific as that

[@djredrover]

@@DrTrefor Woops. Totally missed that playlist. Can't wait to dig in. PS. The length of your videos are bang-on on the "detail vs. bored'm" graph, if you will.

[@j.o.5957]

So (dN/dx - dM/dy) * k_hat gives circulation with the normal in the k_hat direction. Then nabla X F gives all the (dN/dx - dM/dy) * k_hat + (...). dot it by n and you get the tendency to curl around the normal. Take all of that and integrate it over the surface and you get the circulation. Question to self: how to get the normal vectors in the opposite direction? Based on previous observations, I'm assuming we take dM/dy - dN/dx etc. by using the right hand rule.

[@testwest8878]

Hi Dr. Trefor, I recently received a question that required us to use Stoke's Theorem to find the flow rate of the gases escaping through the surface of a sphere with a hole at the bottom. However, it seems that Stoke's Theorem finds the circulation not flux. Why do we use Stoke's Theorem in this case?

[@Jechew]

I’ve been wondering. What application do you use to graph out everything for your videos? I at one point thought it was manual modeling, but apparently not

[@sudiptaroyarts3861]

I'm always telling that you are awesome sir ❤❤❤❤

[@DrTrefor]

I"m always appreciating it:)

[@dhanishcreations7756]

I love you. You are a life saver.

[@TriThom50]

Why does the curl on the interior always cancel? Could we not imagine some vector field that is purely divergent with 0 curl? Similarly, what if the curl is more at certain points than others? How can we use the logic that it will cancel in that case?

[@jaikumar848]

Hello sir ! Could you please tell the the practical application of this theorem?

[@DrTrefor]

Probably the biggest use is in elecricit and magnetism where stokes theorem and divergence theorem are HUGE

[@Chomusuke71]

maxwells equations

[@justadreamerforgood69]

Anything in electromagnetics or fluid mechanics

[@hesammozafarinia8301]

Hi Dr. Trefor, I recently received a question about Stoke's Theorem That is : why that circulation density is just the K(th) component of curl ? , iknow it can proved by the formula of the curl ... but as i understood the curl tells us the circulation of a point then why when we are in xy plane the net circulation is the K component of our curl ?

[@joaocosta3506]

That's because in the xy plane your rotation can only be about the K axis.

[@physicsdiva1871]

Nice explanation

[@abstractnonsense3253]

Reaching the mountain top! 👍

[@DrTrefor]

You know it!

[@gregorsamsa9762]

Thank you so much!

[@bawol-official]

I don’t know if this is the place to ask but I’m about to take my Calc 3 final and I want to ask for ways that I can keep my skills sharp. Is there any mathematical software/calculus visualization sites that can keep me interested once I finish the class?

[@krupt5995]

But there are infinite surface's that can 'support' the same boundary/curve. I suppose this is true for all possible surfaces?

[@madhavkulkarni8980]

Dear Trefor From last ten years I am trying to understand idea behind green & stokes theorem after going through lot of books & websites I unable to capture the concept. So I am very much thankful. Secondly will you please explain cauchys theorem, cauchys integral formula & Riemann mapping theorm which I unable to understand how any deformed region can be transformed to unit circle? wishing all the best for the roject. Thanks again Regards MADHAV KULKARNI M. Sc. ( Maths)

[@jinks908]

*Sits in lecture*: I don’t get it. *Reads textbook*: I still don’t get it *Works through examples*: Still no. *Watches Dr. TB*: Oohhhhhhhh!!!!!

[@robertoberidojr.435]

I love this video

[@christianzabala7839]

Sir. May I ask what software are you using? The one letting you draw on the graph

[@tylermorris5993]

I'm a believer in the almighty stoke

[@kesumanojkumar2074]

Hey need to contact you about subject any possibility

[@salimbenchekroun7543]

Is this how we model Eddy currents?

[@DrTrefor]

absolutely, all this vector calculus stuff is core to understanding fluid dynamics

[@lucaschis4529]

Beautiful 😎

[@ProfessionalAccount-d8c]

What still have problem at is why doting with the normal at each point

[@amanravan9795]

Simply wow

[@AbhinavK-no4ij]

Sir why there is no dxdy instead of dsigma

[@99eigencharu]

becuz we are generalizing to a surface. dxdy is a special case for when the surface is on the xy-plane completely.

[@Nobody-zq8bl]

"Stokes' " implies plural possessive of Stokes, more than one Stokes. It should be Stokes's, but thank you.

[@kakashi8203]

El Professor 🙏

[@dkutlay1282]

you should have said "I'm STOKED for Stokes" :(

[@sukranochani5764]

Nice.

[@DrTrefor]

Thank you! Cheers!

[@danishmalik2295]

Ty

[@master_zenrade]

The one disliker must be insane.

[@DrTrefor]

Hahah agreed!

[@陳帥娃]

good

[@adiej4350]

dude i thought god said he wasnt sending any more prophets / angels down wyd here ????

[@ES-qe1nh]

🎉

[@bartholomeosphinx4382]

Imagine you're listening to a lecture where the lecturer jerks and jumps every 10 seconds.

[@YoungMeasures]

That is why I did not even bother with trying to be fancy with my visuals in my channel! Do animations really enhance math learning?

[@alexeyl22]

Good content with dark background, but your hand waving is truly annoying. Waving hands distracts from focusing on the subject. Please don't do it.

[@seanlinehan8478]

Who asked?

[@ES-qe1nh]

Yuri